# DLM smoothing

### Description

The function apply Kalman smoother to compute smoothed values of the state vectors, together with their variance/covariance matrices.

### Usage

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### Arguments

`y` |
an object used to select a method. |

`...` |
futher arguments passed to or from other methods. |

`mod` |
an object of class |

`debug` |
if |

### Details

The default method returns means and variances of the smoothing
distribution for a data vector (or matrix) `y`

and a model
`mod`

.

`dlmSmooth.dlmFiltered`

produces the same output based on a
`dlmFiltered`

object, typically one produced by a call to
`dlmFilter`

.

The calculations are based on the singular value decomposition (SVD) of the relevant matrices. Variance matrices are returned in terms of their SVD.

### Value

A list with components

`s` |
Time series (or matrix) of smoothed values of the state vectors. The series starts one time unit before the first observation. |

`U.S` |
See below. |

`D.S` |
Together with |

### Warning

The observation variance `V`

in `mod`

must be nonsingular.

### Author(s)

Giovanni Petris GPetris@uark.edu

### References

Zhang, Y. and Li, X.R., Fixed-interval smoothing algorithm
based on singular value decomposition, *Proceedings of the 1996
IEEE International Conference on Control Applications*.

Giovanni Petris (2010), An R Package for Dynamic Linear
Models. Journal of Statistical Software, 36(12), 1-16.
http://www.jstatsoft.org/v36/i12/.

Petris, Petrone, and Campagnoli, Dynamic Linear Models with
R, Springer (2009).

### See Also

See `dlm`

for a description of dlm objects,
`dlmSvd2var`

to obtain a variance matrix from its SVD,
`dlmFilter`

for Kalman filtering,
`dlmMLE`

for maximum likelihood estimation, and
`dlmBSample`

for drawing from the posterior distribution
of the state vectors.

### Examples

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